where n t is the number of time steps in the
averaging window and σ DRM is the lesser ofσ 12 and σ 23 at each point
in time. An efficient algorithm to minimize SEDRM is to
locate the moment of minimum σ DRM, compute the
SEDRM for time windows of varying width around the
moment and choose the width that gives the smallest
SEDRM. We tested a variety of values forn t.
Note that all equations were derived from Marshall’s (1958) model (Eqn.1 ) under the assumption of an instantaneous heat pulse, whereas
in reality the heat pulse occurs has a finite pulse length oft 0. We corrected for this by shifting each
temperature timecourse by -t 0/2 before applying
Eqn. 1 . The effect of this treatment is shown in Supporting
Information (SI) Notes S1 and Fig. S1 .
2.2 Theoretical test of the DRM, HRM, CHPM and Tmax methods
2.2.1 Comparison of heat-pulse based methods
To assess the theoretical viability of the DRM in comparison to other
heat pulse methods, and to help optimize operational considerations such
as the size and timing of averaging window(s), we used Eqn. 1to simulate timecourses of temperature following a heat pulse. We
compared the predicted values of V DRM (Eqn.7 ) with V HRM (Eqn. 4 ), and also
with two other estimates of V , based, respectively, on the CHPM
(SR Green & Clothier, 1988) and the Tmax method (Cohen et al., 1981) as
modified by Kluitenberg and Ham (2004). In the CHPM, sap velocity is
calculated at the time point (t C(1,3)) when the
temperature rises for Probe #1 and #3 are equal, so that the ratio of
temperature rises is unity and the logarithmic term in Eqn. 4disappears, giving sap velocity as